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Find the distance between the following pair of points:
$(-6, 7)$ and $(-1, -5)$
Given:
The given pair of points is $(-6, 7)$ and $(-1, -5)$.
To do:
We have to find the distance between the given pair of points.
Solution:
We know that,
The distance between two points \( \mathrm{A}\left(x_{1}, y_{1}\right) \) and \( \mathrm{B}\left(x_{2}, y_{2}\right) \) is \( \sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}} \)
Therefore,
The distance between the points $(-6,7)$ and $(-1,-5)$\( =\sqrt{[-1-(-6)]^{2}+(-5-7)^{2}} \)
\( =\sqrt{(-1+6)^{2}+(-5-7)^{2}} \)
\( =\sqrt{(5)^{2}+(-12)^{2}} \)
\( =\sqrt{25+144} \)
\( =\sqrt{169} \)
\( =13 \)
The distance between the given pair of points is $13$ units.
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